相关论文: Alternative Metrics
Secure communication protocols are often formulated in a paradigm where the message is encoded in measurement outcomes. In this work we propose a rather unexplored framework in which the message is encoded in measurement settings rather…
This text is a survey on symmetric matrices. It serves as a script for a module to be taught at university.
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
In the paper the method for estimation of throughput metrics like available bandwidth and end-t-end capacity is supposed. This method is based on measurement of network delay $D_i$ for packets of different sizes $W_i$. The simple expression…
The purpose of this paper is to give, on one hand, a mathematical exposition of the main topological and geometrical properties of geometric transitions, on the other hand, a quick outline of their principal applications, both in…
Formal definitions of quantities, quantity spaces, dimensions and dimension groups are introduced. Based on these concepts, a theoretical framework and a practical algorithm for dimensional analysis are developed, and examples of…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.
While the methodological rigor of computing research has improved considerably in the past two decades, quantitative software engineering research is hampered by immature measures and inattention to theory. Measurement-the principled…
The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…
This monograph presents a class of algorithms called coordinate descent algorithms for mathematicians, statisticians, and engineers outside the field of optimization. This particular class of algorithms has recently gained popularity due to…
Integrating text and numbers effectively is a crucial step towards enhancing Large Language Models (LLMs) capabilities in assisting in scientific tasks. While most current approaches rely on discrete tokenization of numbers, for instance,…
Work in progress concerning alternative formalizations of arithmetic.
We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.
Optical multiplexing is a key technique that enhances the capacity of optical systems by independently modulating various optical parameters to carry distinct information. Among these parameters, wavelength, polarization, and angle are the…
This article aims to provide a brief overview of both established and novel ellipsometry techniques, as well as their applications. Ellipsometry is an indirect optical technique in that information about the physical properties of a sample…
This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…
The concept of angle, angle functions, and the question how to measure angles present old and well-established mathematical topics referring to Euclidean space, and there exist also various extensions to non-Euclidean spaces of different…
Performance metrics (error measures) are vital components of the evaluation frameworks in various fields. The intention of this study was to overview of a variety of performance metrics and approaches to their classification. The main goal…
Software metrics offer a quantitative basis for predicting the software development process. In this way, software quality can be improved very easily. Software quality should be achieved to satisfy the customer with decreasing the software…